In this paper, we present an efficient numerical algorithm for solving singular two-point linear and non-linear problems, which is based on the Modified Adomian Decomposition Method (MADM). Also, we proposed a new operator for solving singular boundary value problems (BVPs), which gives lesser error compared to MADM and other existing techniques given in the literature, at neighborhood of the right boundary. To illustrate its effectiveness, the algorithm is tested on two linear and two non-linear examples, and the results obtained using Mathematica 6.0 demonstrate the reliability and efficiency of the proposed algorithm.